SIAM Journal on Computing
Asymptotic enumeration of Latin rectangles
Journal of Combinatorial Theory Series B
Chord: A scalable peer-to-peer lookup service for internet applications
Proceedings of the 2001 conference on Applications, technologies, architectures, and protocols for computer communications
Peer-to-peer networks based on random transformations of connected regular undirected graphs
Proceedings of the seventeenth annual ACM symposium on Parallelism in algorithms and architectures
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
Sampling Regular Graphs and a Peer-to-Peer Network
Combinatorics, Probability and Computing
Fast approximation of the permanent for very dense problems
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Maintaining the Ranch topology
Journal of Parallel and Distributed Computing
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We present a family of peer-to-peer network protocols that yield regular graph topologies having known Hamilton cycles. These topologies are equivalent, in a well-defined sense, to the random regular graph. As a consequence, we have connectivity deterministically, and logarithmic diameter and expansion properties with high probability. We study the efficacy of certain simple topology-altering operations, designed to introduce randomness. These operations enable the network to self-stabilise when damaged. They resemble the operations used by Cooper, Dyer and Greenhill (2007) for a similar purpose in the case of random regular graphs. There is a link between our protocols and certain combinatorial structures which have been studied previously, in particular discordant permutations and Latin rectangles. We give the first rigorous polynomial mixing-time bounds for natural Markov chains that sample these objects at random. We do so by developing a novel extension to the canonical path technique for bounding mixing times: routing via a random destination. This resembles a technique used by Valiant (1982) for low-congestion routing in hypercubes.